1. Field of the Invention
This invention relates to improvements in passive methods for determining the position of a moving observer with respect to a remote object or objects, and more particularly to improvements in such methods for enabling vehicular maneuvering with respect to remote objects for robotic control, navigation, and the like.
2. Description of the Prior Art
The problem of passively determining the position of a moving object with respect to a surrounding object or objects has long been vexatious. This is so because ambiguities which often enter into calculations and measurements usually cannot be controlled. This can be seen for example in considering an observer who is moving along a path directly toward a remote object and who takes a sequence of angular measurements to the remote object with respect to, for instance, a fixed x-y-z coordinate frame. It will be seen that the measurements which are taken are constant, and, therefore, the location of the remote object is indeterminate.
In addition, in making such angular measurements, there is always the possibility of error with respect to each measurement. It can be seen that if, for example, two angular measurements were made, each with some finite error factor, the true angles could be expressed as being only within plus or minus some error amount on either side of the measured angles. The object, therefore, can only be located somewhere within an area defined by the angular deviations of the error from the measured angles.
Many solutions to this problem have been suggested in the past; however, none enable the possibility of reducing the computational requirements to a level which would make real time vehicle control feasible, at least to the extent is achievable by, for example, by present active navigational devices. In addition, even with the fast digital processing equipment becoming ever increasingly available and lower in cost, the computation time required to process the great quantities of data generated by previous solutions to this problem has precluded serious consideration of passive position determination as being impractical in most real time applications.
More specifically, in dealing with the data generated by in making such measurements, many problems have been confronted by investigators in the past. For example, it has been proposed to apply recursive Kalman-Bucy filter techniques to matrix representations of the data. The Kalman-Bucy filter techniques, however, require the application of certain linearization assumptions, as well as system initializations, and result in a large computional burden, requiring large, fast computing support. The initializations mentioned include, among other things, a requirement for the inputting of a first estimate of the position of the remote object together with the inputting of the allowable error deviation permitted in the difference between the actual position and the estimated position. This can result, in certain cases, in the technique being unable to produce an accurate estimate of the position of the remote object, if, for example, the original position estimate is outside the permitted deviation. That is to say, in some cases, the Kalman-Buch filter fails to converge on an answer representing the location of the remote object. This makes real-time position analysis difficult, if not impossible in certain applications.
On the other hand, least-squares approaches have been considered; for example, the so-called Moore-Penrose pseudo-matrix-inverse technique has been considered by some investigators. The Moore-Penrose technique can be applied either recursively or non-recursively. When the Moore-Penrose technique is applied recursively, the result is similar to, and in some cases equivalent to, the Kalman-Bucy filter technique. In contrast, in the past, investigators have almost universally rejected the non-recursive application of the Moore-Penrose technique because the calculation of the matrix products required by the technique appear to result in an unhandleable growth in the number and complexity of calculations, especially in consideration of the large quantities of data representing numerous position measurements for accurate determinations, as discussed above. This apparent growth would appear to require the support of a large computational capability, which may significantly impact the cost of implementing such a scheme. Again, the large computional burden resulting from the application of the technique precludes its use in many real-time applications The Moore-Penrose pseudo-matrix-inverse technique, however, does have distinct advantages in that it requires no initialization and linearizing assumptions.
It should be also noted that coming of interest recently are digital topographical map concepts in which the features of a particular terrain or surface of interest are represented by digitized quantities which can be plotted or otherwise used to represent the terrain or surface. Such digital map concepts are described, for example, in "Airborne Electronic Map Systems, Part I - Design", Proc. IEEE, NAECON Conference, 1981, by Gerald O. Burnham, and "Airborne Electronic Map Systems, Part II- Applications", supra. Additionally, the application of the techniques of this invention to terrain following, terrain avoidance problems is described in copending patent application entitled METHOD FOR PASSICE TERRAIN FOLLOWIND AND AVOIDANCE, Ser. No. 568,677, filed Jan. 6, 1984, currently pending, and assigned to the assignee hereof, said application being incorporated by reference herein.
In attempts to achieve navigational abilities of vehicles (vehicles being used herein to denote generally any movable object, such an aircraft, ship, missile, car, robot etc.) by sensing the local terrain, usually some form of active device is considered. In the case of aircraft, for instance, terrain following radars are used in which radio signals are transmitted, usually forwardly and downwardly, from an aircraft, and the time at which the echo is received and the direction from which it arrives are processed to ultimately determine the location of the underlying terrain or surface with respect to the aircraft. Aside from sending electromagnetic signals outside the vehicle, such devices may not be forward looking, and are capable of detecting only changes in altitude of the aircraft with respect to the ground directly underneath it. This has the disadvantage of not being able to detect sudden rises in terrain, and makes the use of the device limited to areas only in which gradual or predictable terrain changes exist.
Passive devices capable of forward or downward looking exist in which a picture of the terrain directly in front of a vehicle (or in some convenient direction with respect to the vehicle) is generated. An example of such device is a forward looking infrared receiver (FLIR), and in fact, the method of the present invention can be practiced in conjunction with signals generated by such FLIR, although it will be appreciated that in fulfilling an object of the invention of achieving passive position information, such FLIR signals in some instances may be discarded in favor of other passive signal generation means, such as television signals or the like, as will become apparent below.